I can solve almost all my textbook problems related to current electricity using formulas but it seems in the end, I don't understand what current is. The bookish definition of current is:
Current is defined to be the amount of charge passed through a cross sectional area of a conductor per unit time.
I want to know, if how I think of current is right and, if possible, I would very much appreciate, if a better way of thinking current is provided.
Let us take a conductor and fix a cross sectional area and suppose there are $n$ free electrons on one side of the cross section which will eventually hit the cross section. We take a stop watch in our hand. And now when the electrons start moving, we start the stop watch. Now the electrons will randomly hit the cross section one by one or a few at once. After $1$ second, we stop the timer. We see that $x$ electrons have gone penetrating that cross section. Since charge of each electron is $e$,then $xe$ charge has flown in that one second. So current will be $xe$ A.
Is my line of thought correct? Specially do the points marked in italics matter? or just somehow the number of electrons penetrating that cross section in one second matter?